Generalized stochastic model for molecular rotational motion in dense media

We introduce a general stochastic model that encompasses all other commonly used stochastic models for the orientational motion of molecules in dense media. In this model the rotational motion is envisaged to proceed by an alternating sequence of collision and between collision events. These events are characterized by transition probabilities whose form can be chosen in accordance with the physical situation. The durations of the events are governed by probability density functions. These probability densities enable us to investigate the effects of finite durations of collisions and of time correlations between successive collisions. The effect of correlations between successive collisions is to produce nonexponential behavior in the time correlation functions of orientational variables. Indeed these time correlation functions can become negative and can have damped oscillatory behavior even in the complete absence of explicit inertial effects (free rotations). The finite duration of collisions insures that the short time expansion of the time correlation function does not diverge to any order in the time. In addition, we show that in dense gases and liquids with reasonable assumptions our model results agree well with exact molecular dynamics calculations to at least order t5. We also discuss the relation between the stochastic approach and the memory function approach.